Kevin is 24 years older than Umaima. Fifteen years ago, Kevin was 5 times as old as Umaima. How old is Umaima now?
Explanation: We can use the given information to write down two equations that describe the ages of Kevin and Umaima. Let Kevin's current age be $k$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $k = u + 24$ Fifteen years ago, Kevin was $k - 15$ years old, and Umaima was $u - 15$ years old. The information in the second sentence can be expressed in the following equation: $k - 15 = 5(u - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: $k = u + 24$ . Substituting this into our second equation, we get the equation: $(u + 24)$ $-$ $15 = 5(u - 15)$ which combines the information about $u$ from both of our original equations. Simplifying both sides of this equation, we get: $u + 9 = 5 u - 75$ Solving for $u$ , we get: $4 u = 84$ $u = 21$.